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Estimates for the First Eigenvalue of \({\mathfrak {L}}\)-Operator on Self-shrinkers

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Abstract

In this paper, we investigate the Dirichlet and Neumann eigenvalue problems in bounded domains on a complete self-shrinker, then we get some lower bound estimates for the first non-zero eigenvalue of \({\mathfrak {L}}\).

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Acknowledgements

The author expresses his sincere thanks to the referees and editors for their careful reading of the original manuscript and for their comments which improved the paper. This work was completely supported by the Natural Science Foundation of China(Grant No. 12026262) and Nankai Zhide Foundation.

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Authors and Affiliations

  1. Department of Applied Mathematics, Anhui University of Technology, Maanshan, 243002, People’s Republic of China

    Yecheng Zhu

  2. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, People’s Republic of China

    Yecheng Zhu

  3. Chern Institute of Mathematics, Nankai University, Tianjin, 300071, People’s Republic of China

    Yecheng Zhu

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  1. Yecheng Zhu
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Correspondence to Yecheng Zhu.

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Zhu, Y. Estimates for the First Eigenvalue of \({\mathfrak {L}}\)-Operator on Self-shrinkers. Results Math 76, 216 (2021). https://doi.org/10.1007/s00025-021-01533-z

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  • DOI: https://doi.org/10.1007/s00025-021-01533-z

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